6. Interpolation Functions
6.11 Exponential Function Interpolation; G02.3, G03.3
81
Machining example
•
Example of uniform helix machining of taper shape
i1
j1
x1
x0 x2
p1
A axis
r1
r2
z1
z2
z0
X axis
Z axis
<Relational expression of exponential function in machining example>
Z (
θ
) = r1
∗
(e
θ
/D
-1)
∗
tan (p1) / tan (i1) + z0
... (1)
X (
θ
) = r1
∗
(e
θ
/D
-1) / tan (i1)
... (2)
A (
θ
) = (-1)
ω
∗
360
∗
θ
/ (2
π
)
D = tan (j1) / tan (i1)
Z (
θ
)
Absolute value from zero point of Z axis (axis that linearly interpolates between interval
with linear axis (X axis))
X (
θ
)
Absolute value from X axis (linear axis) start point
A (
θ
)
Absolute value from A axis (rotation axis) start point
r1
Exponential function interpolation constant value (address R command)
r2
Workpiece left edge radius
x2
X axis (linear axis) position at workpiece left edge
x1
X axis (linear axis) end point (address X command)
x0
X axis (linear axis) start point (Set as "x0
≤
x1" so that workpiece does not interfere with
tool)
z1
End point of Z axis (axis that linearly interpolates between interval with linear axis (X
axis)) (address Z command)
z0
Start point of Z axis (axis that linearly interpolates between interval with linear axis (X
axis))
i1
Taper gradient angle (address I command)
p1
Slot base gradient angle
j1
Torsion angle (helix angle) (address J command)
ω
Torsion direction (0: Forward rotation, 1: reverse direction)
θ
Workpiece rotation angle (radian)
f1
Initial feedrate (address F command)
q1
Feedrate at end point (address Q command)
k1
Insignificant data (address K command)
According to expressions (1) and (2):
Z (
θ
) = X (
θ
)
∗
tan (p1) + z0
... (3)
According to expression (3), the slot base gradient angle (p1) is determined from the X axis and Z
axis end point positions (x1, z1).
The Z axis movement amount is determined by the slot base gradient angle (p1) and X axis
position.
In the above diagram, the exponential function interpolation's constant value (r1) is determined with
the following expression using the workpiece left edge radius (r2), X axis start point (x0), X axis
position at workpiece left edge (x2) and taper gradient angle (i1).
r1 = r2 - { (x2 - x0)
∗
tan (i1) }
... (4)
